1. Field of the Invention
The present invention relates generally to the field of computer animation. More particularly, the present invention relates to a system and method for generating computer animated graphical images of a vascular structure attached to an anatomical structure.
2. Description of the Prior Art
Computer animation techniques have been used for generating animated images of animal bodies including human bodies. For various applications in the field of medicine, including medical training, it is useful to generate animated images of various anatomical elements of an animal such as bones, muscles, vascular tissue, and other tissue. Such animated images are also useful in special effects applications for motion pictures.
The present application is concerned primarily with generating computer animated images of a vascular structure attached to an anatomical structure (e.g., bones, muscles, and other tissue) as the anatomical structure moves in accordance with an animated sequence. Prior art methods for generating computer animated images of a layer of skin superimposed over an underlying structure provide some background information for the development of computer animated images of a vascular structure. However, as further explained below, special problems arise in modeling a vascular structure attached to an anatomical structure that do not arise in modeling a layer of skin superimposed over an underlying anatomical structure.
Anatomically Based Modeling is discussed in detail in an article of the same title written by Jane Wilhelms and Allen Van Gelder of the University of California, Santa Cruz, and published in Computer Graphics Proceedings, Annual Conference Series, 1997. This reference describes a method for modeling skin deformation in response to deformation of anatomical elements which are modeled as triangle meshes or ellipsoids. Skin overlying the anatomical elements is modeled by a triangle-mesh of skin vertices which is attached to the anatomical elements by anchors.
The anatomically based modeling process described by Wilhelms and Van Gelder includes the steps of: defining springs between associated skin vertexes of the triangle-mesh skin; binding each skin vertex with a closest anatomical body component (muscle, bone, or generalized tissue) in accordance with an anchoring method; animating the anatomical body causing the anatomical body components to be moved; moving the skin vertexes of the triangle-mesh skin based on the movement of the body components and the anchoring, the movement causing corresponding springs to deform and therefore exert restoring forces on the skin vertexes; and resolving the spring forces during a relaxation phase of the process.
The springs, which are mathematical functions defining a potential force between the associated vertices as a function of the distance therebetween, provide for achieving a natural elasticity in the skin as it stretches over the animated understructure.
Wilhelms and Van Gelder describe a binding phase in the above cited reference wherein selected points of the layer of skin are bound to associated points on the underlying anatomical structure. An anchor of a particular skin vertex is defined to be the nearest point on its underlying component. A virtual anchor, defined as the initial position of a skin vertex relative to its anatomical component, is the position of the vertex when the skin is extracted in the animal""s rest position. The anchors and virtual anchors are stored parameterized in the local space of the component. As shape changes occur in the anatomical components, the skin vertices are correspondingly affected via the anchors and virtual anchors. Each skin vertex is considered to be bound to its virtual anchor.
Special problems arise in binding a vascular structure to an anatomical structure that do not arise in binding a layer of skin to an anatomical structure primarily because a vascular structure has a substantially cylindrical surface, and a substantially circular transverse cross section, while a layer of skin has a substantially planar, albeit curved, surface. As muscles flex and skeletal elements are moved during animation, it is desirable that the vascular tissue attached thereto have an elastic quality in order to appear natural. It is also very important that the vascular structures not be flattened as they are flexed and bent during movement of the anatomical structures. However, if a vascular structure is bound to an anatomical structure in accordance with the method described by Wilhelms and Van Gelder, the vascular structure is flattened during animation of the underlying anatomical structure.
Another problem associated with the anatomically based modeling process described by Wilhelms and Van Gelder is that the exterior object, that is the layer of skin, is modeled using a triangle mesh of vertices. Polygonal models such as a triangle mesh of vertices are useful primarily for representing objects having flat surfaces, but fall short in allowing the degree of flexibility required for representing curved bodies having complex details. By contrast, parametric surfaces afford great flexibility by providing modelers with intuitive control parameters that make manipulating them fairly natural. Many different types of parametric surfaces, or patches, are commonly used by modelers for representing curved surfaces. One type of parametric surface commonly used by modelers is the non-uniform rational B-spline surface (NURBS) patch. A NURBS patch has a resolution defined by an associated number of control vertex (CV) points which are arranged in an array and which provide a xe2x80x9ccontrol hullxe2x80x9d of the patch.
In order to achieve optimal realism in computer animated images of a vascular structure, it is desirable to be able to model a vascular structure using parametric surfaces which provide a high degree of flexibility. It would also be desirable to provide an anatomically based modeling process having the advantages of the process described by Wilhelms and Van Gelder, but using a parametric surface model for the vascular structure, wherein the parametric surface is formed by a plurality of patches some of which have different resolutions defined by a different number of CV points.
What is needed is a system and method for generating realistic animated graphical images of a vascular structure stretching attached to an animated anatomical structure, wherein the vascular structure is modeled by parametric surface patches, wherein the vascular structure may have an elastic quality, and wherein the transverse cross section of the vascular structure is not flattened during animation.
It is an object of the present invention to provide a system and method for generating realistic animated graphical images of a vascular structure attached to an animated anatomical structure, wherein the vascular structure is modeled by parametric surface patches, wherein the vascular layer may have an elastic quality, and wherein the transverse cross section of the vascular structure is not flattened during animation.
Briefly, a presently preferred embodiment of the present invention provides a process for generating animated graphical images of a vascular structure attached to an anatomical structure. The process includes the steps of: generating and arranging a plurality of anatomical patches in rest positions to form an anatomical patch surface representing an anatomical structure disposed in a rest position; and generating and arranging at least one vascular patch over the anatomical structure in the rest position, the vascular patch having an associated array of control points configured to form a closed surface of a vascular structure having a closed transverse cross section. In one embodiment, the control points of each of the vascular patches are configured to form a substantially cylindrical surface of a vascular structure having a substantially circular transverse cross section.
The process also includes the step of establishing a binding positional relationship between at least a portion of the control points and the anatomical patch surface by determining binding points on the surface of at least one selected anatomical patch in a rest position. In accordance with the present invention, the control points of each vascular patch include at least one transverse cross-sectional subset of control points that are disposed proximate an associated transverse cross-section of the vascular structure, each control point of the subset having a common binding point. The common binding point is located on a closest point on the surface of the selected anatomical patch to a selected one of the control points of the transverse cross-sectional subset.
The process further includes the steps of: animating the anatomical structure causing a translation in the position of the selected anatomical patch relative to the rest position, and resulting in a translated anatomical patch surface; and deforming the vascular patch by moving at least a portion of the control points of the vascular patch based on the associated binding positional relationships and the translation in the position of the selected anatomical patch.
In an embodiment, at least one intra-patch spring may be defined between a corresponding pair of selected control points of at least one of the vascular patches. Each intra-patch spring defines a potential force between the corresponding pair of selected control points. The step of deforming the vascular patch by moving at least a portion of the control points results in at least a portion of the springs being deformed causing spring restoring forces to be exerted on associated ones of the control points. Spring restoring forces are computed and resolved to determine a relaxed position for each of the control points.
The step of establishing a binding positional relationship between each of the control points and the associated closest anatomical patch in the rest position further includes determining an anchor point associated at least a portion of the control points. Each anchor point defines the location of the associated control point relative to its associated binding point with the associated closest anatomical patch being disposed in the rest position. The step of moving each of the control points based on the binding positional relationships further includes determining a moved position for each of the control points based on the associated binding point, the associated anchor point, and a displacement in the position of the associated closest anatomical patch.
In an embodiment, each of the anatomical patches is a non-uniform rational B-spline (NURBS) patch having a (u,v) coordinate system defining a u-direction and a v-direction relative to the NURBS patch. In this embodiment, the step of determining an anchor point associated with each of the control points of the subset further includes: determining a normal vector that is normal to the surface of the associated closest anatomical patch at the associated binding point; determining a u-tangent to the surface of the associated closest anatomical patch along the u-direction at the associated binding point; determining a v-tangent to the surface of the associated closest anatomical patch along the v-direction at the associated binding point, the normal vector, the u-tangent, and the v-tangent defining an associated binding point reference coordinate system for the associated anchor point; and defining the position of the anchor point relative to the binding point using the associated binding point reference coordinate system.
The step of establishing a binding positional relationship further includes the step of generating and storing anchor point mapping information associated with each of the vascular control points. The anchor point mapping information includes: patch information indicative of the associated selected anatomical patch; binding point information indicative of the associated binding point; and anchor point position information indicative of the position of the anchor point relative to the binding point in terms of the associated binding point reference coordinate system of the associated selected anatomical patch in the rest position.
The step of moving each of the control points based on the associated binding positional relationship includes: reading the patch information and the binding point information associated with a particular one of the control points; determining a displaced binding point reference coordinate system by determining a displaced normal vector, a displaced u-tangent, and a displaced v-tangent to the surface of the associated selected anatomical patch at the associated binding point with the selected anatomical patch being in the displaced position relative to the associated rest position; reading the anchor point position information associated with the particular control point; and determining a moved position of the particular control point based on the anchor point position information and the displaced reference coordinate system.
An important advantage of the system and method of the present invention is that it provides for generating high quality graphical images of a vascular structure attached to an animated anatomical structure, wherein the vascular structure is modeled by parametric surface patches, wherein the vascular layer may have an elastic quality, and wherein the transverse cross section of the vascular structure is not flattened during animation.
The foregoing and other objects, features, and advantages of the present invention will be apparent from the following detailed description of the preferred embodiment which makes reference to the several figures of the drawing.